Question

Sweet Inc. manufactures cycling equipment. Recently, the vice president of operations of the company has requested construction of a new plant to meet the increasing demand for the company’s bikes. After a careful evaluation of the request, the board of directors has decided to raise funds for the new plant by issuing $3,201,000 of 9% term corporate bonds on March 1, 2017, due on March 1, 2032, with interest payable each March 1 and September 1, with the first interest payment on September 1st, 2017. At the time of issuance, the market interest rate for similar financial instruments is 8%.

Answer 1

selling price of bonds = [Present value of annuity factor * (interest payment) ] + [present value factor * (face value)]

here,

present value of annuity factor = [1 - (1+r)^(-n)] / r

here,

r = market interest rate =>8% =>0.08.per annum =>0.08/2 =>0.04.

n = number of periods => 15 years * 2 semi annual periods = 30 periods.

=>[1 - (1.04)^(-30)]/0.04

=> 17.292032

interest payment = face value * stated interest rate *1/2

=>$3,201,000 * 9% *1/2

=>$144,045.

present value factor = 1 /(1+r)^n

=>1 /(1.04)^30

=>0.30831867.

face value of bond = $3,201,000

now.

the selling price of bond = [$144,045 *17.292032] + [$3,201,000*0.30831867]

=>$2,490,830.75 + 986,928.063.

=>$3,477,758.81.

the given bonds must be selling at $3,477,758.81.